Dynamics of a Delayed HIV-1 Infection Model with Saturation Incidence Rate and CTL Immune Response

Abstract

In this paper, we investigate the dynamics of a five-dimensional virus model incorporating saturation incidence rate, CTL immune response and three time delays which represent the latent period, virus production period and immune response delay, respectively. We begin this model by proving the positivity and boundedness of the solutions. Our model admits three possible equilibrium solutions, namely the infection-free equilibrium [Formula: see text], the infectious equilibrium without immune response [Formula: see text] and the infectious equilibrium with immune response [Formula: see text]. Moreover, by analyzing corresponding characteristic equations, the local stability of each of the feasible equilibria and the existence of Hopf bifurcation at the equilibrium point [Formula: see text] are established, respectively. Further, by using fluctuation lemma and suitable Lyapunov functionals, it is shown that [Formula: see text] is globally asymptotically stable when the basic reproductive numbers for viral infection [Formula: see text] is less than unity. When the basic reproductive numbers for immune response [Formula: see text] is less than unity and [Formula: see text] is greater than unity, the equilibrium point [Formula: see text] is globally asymptotically stable. Finally, some numerical simulations are carried out for illustrating the theoretical results.